A secondary school student's development of geometric thought during instruction was investigated using the P. M. van Hiele (1986) model and dynamic computer software, the Geometer's Sketchpad (Key Curriculum Press, 1993). During a 21-hr study, the author used a clinical interview procedure to determine a student's predominant level of thought and to gain an in-depth understanding of the developmental process of geometric reasoning. Ordered from the simplest to the most complicated, the 4 learning stages-intuitive, analytical, inductive, and deductive leaming-were identified in terms of symbol, signal, and "implicatory" properties. The use of active visualization with the dynamic software facilitated the movement from symbol to signal and then to implicatory character.he ideas of van Hiele (1 986) have been a catalyst for
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